Answer
Option (b)
Work Step by Step
RECALL:
(1) $\log_a{P} -\log_a{Q} = \log_a{\left(\dfrac{\log_a{P}}{\log_a{Q}}\right)}$
(2) $\log_a{P} + \log_a{Q} = \log{(PQ)}$
(3) $\log_a{P^n}=n\cdot \log_a{P}$
Use rules (1) and (3) above to obtain:
$=\log_a{\left(\dfrac{x}{y}\right)}+\log_a{z^2}$
Use rule (2) above to obtain:
$=\log_a{\left(\dfrac{x}{y} \cdot z^2\right)}
\\=\log_a{\left(\dfrac{xz^2}{y}\right)}$
Thus, the answer is Option (b).
